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The one-dimensional Bose-Fermi-Hubbard model in the ultrafast-fermion limit: Charge density wave phase and MI - CDW phase separation

In a recent work [1] we presented results for the Bose-Fermi-Hubbard model (BFHM) in the limit of ultrafast fermions. The present work gives an overview over the used methods and an deeper insight into the implications arising from the treated limit. Starting from the discussion of the phase diagram obtained by numerical means, we develop an analytic theory and derive an effective bosonic Hamiltonian. Arising issues in the Hamiltonian are overcome by inclusion of a back-action, renormalizing the solution of our system. Based on a detailed analysis of the effective Hamiltonian, the phase diagram in the thermodynamic limit is constructed by analytic means and comparison to numerical results obtained by density matrix renormalization group (DMRG) techniques for the full BFHM shows a very reasonable agreement. The most prominent feature of the phase diagram, the existence of a phase separation between Mott insulator (MI) and charge density wave (CDW) is discussed in depth with inclusion of important effects due to the boundary condition.